DIELECTRIC-RELAXATION OF LIQUID-MIXTURES

General expressions in terms of van Hove time correlation functions are given for the wave vector frequency-dependent dielectric function of multicomponent mixtures. The van Hove functions are obtained by applying the Kerr approximation and the dielectric relaxation at zero wave vector is considered in detail. At this level of theory, the frequency-dependent dielectric constant depends upon the self-reorientational correlation times of the various species involved and upon the equilibrium pair correlation functions. It is shown that if the self-correlation times are assumed to be given by the Stokes-Debye relationship, and if the equilibrium direct correlation functions obey certain relatively weak conditions, then for particles of equal size (i.e., the self-correlation times are the same for all species) the dielectric relaxation behavior can be described by a simple Debye formula with a single concentration-dependent relaxation time. This observation is independent of the number of components, of the concentration, and of the molecular dipole moments of the different species present. It may help explain why for some binary mixtures of polar molecules experimental measurements indicate only a single relaxation channel. The exact Kerr result for binary mixtures is expressed explicitly as the sum of two Lorentzians, and some numerical results are given for solutions of dipolar hard spheres of different diameter.